Infinite truth assignments I've been trying to solve the following problem, but I am running out of ideas. The problem is:  Is there a set $\Gamma \subset \mathcal{L}_0$ and an enumeration of an infinite set of truth assignments $v_1, v_2, \ldots$ such that for every truth assignment $v$, $v$ satisfies all the formulas in $\Gamma$ if and only if there is an $i$ such that $v = v_i$?    I tried to generate a contradiction using an argument similar to that one of Cantor to prove that rational numbers are countable, but it failed. Please I would appreciate any help. Thanks!
Countable set of truth assignments satisfying set of well formed formulas I am trying to answer the following question posed in my logic class: (throughout we work in propositional logic) is there a set $S$ of well-formed-formulas (wffs) satisfied by countable set $V$ of truth assignments such that any truth assignment satisfying $S$ lies in $V$?    My guess is no.  My first reaction to this was to do a diagonalization.  Present $V$ as an array with $v_{i, j}$ the truth value that assignment $v_i$ gives to the $j$-th propositional letter.  Obviously the hard case is when $S$ is infinite; if $S$ is finite, then only finitely many propositional letters occur in the $S$-formulae.  Then there is some maximal $k$ for which all $A_n$ with $n \geq k$ do not occur in V.  Then the diagonalization is trivial: just diagonalize from the $k$-th letter onward, since changing $A_k$ in this range doesn't affect anything in $S$.  But I have little clue about how to approach the main case when $S$ is infinite. I thought maybe I should try using the fact that $S$ is consistent (since it's satisfiable).  If it's maximally consistent, then I think this is simple too, since for every propositional letter $A_n$, either $A_n$ is in $S$ or $(\neg A_n)$ is in $S$, implying that there is only one truth assignment satisfying $S$--since every truth assignment must agree on each propositional letter.    But if $S$ is not maximally consistent, this isn't available to me.  Somehow I would like to show that infinitely many propositional letters do not occur in $S$.  Then I can apply the trick above and just diagonalize through the superfluous letters.    So, yes, just looking for some hints or corrections if you have any please, though maybe if I don't get anywhere on my own I'll give up and ask for more.  Thanks.  (By the way, by referring to letters that "occur in $S$" I mean letters that occur in some formula in $S$).
Installing Crystal Reports 8.5 on Windows 7 I have successfully installed Crystal Reports 8.5 on my Windows 7 desktop, but when I try to launch the application i get this:    Any experience with this?  Besides the obvious "update to as newer version", does anyone have any suggestions? .NET OpenSource projects and strong named assemblies? Although the merits of stepwise model selection has been discussed previously, it is becoming unclear to me what exactly is "stepwise model selection" or "stepwise regression". I thought I understood it, but not so sure anymore.  My understanding is that these two terms are synonymous (at least in a regression context), and that they refer to the selection of the best set of predictor variables in an "optimal" or "best" model, given the data. (You can find the Wikipedia page , and another potentially useful overview .)    Based on several previous threads (for example here: ), it appears that stepwise model selection is considered a cardinal sin. And yet, it seems to be used all the time, including by what seem to be well respected statisticians. Or am I mixing up the terminology?  My main questions are:   By "stepwise model selection" or "stepwise regression", do we mean: A) doing sequential hypothesis testing such as likelihood ratio tests or looking at p-values? (There is a related post here: ) Is this what is meant by it and why it is bad? Or B) do we also consider selection based on AIC (or similar information criterion) to be equally bad? From the answer at , it appears that this too is criticized. On the other hand, Whittingham et al. (2006; )1 seems to suggest that variable selection based on information-theoretic (IT) approach is different from stepwise selection (and seems to be a valid approach)...?  And this is the source of all my confusion.  To follow up, if AIC based selection does fall under "stepwise" and is considered inappropriate, then here are additional questions: If this approach is wrong, why is it taught in textbooks, university courses, etc.? Is all that plain wrong? What are good alternatives for selecting which variables should remain in the model? I have come across recommendations to use cross-validation and training-test datasets, and LASSO.   I think everyone can agree that indiscriminately throwing all possible variables into a model and then doing stepwise selection is problematic. Of course, some sane judgement should guide what goes in initially. But what if we already start with a limited number of possible predictor variables based on some (say biological) knowledge, and all these predictors may well be explaining our response? Would this approach of model selection still be flawed? I also acknowledge that selection of the "best" model might not be appropriate if AIC values among different models are very similar (and multi-model inference may be applied in such cases). But is the underlying issue of using AIC-based stepwise selection still problematic?  If we are looking to see which variables seem to explain the response and in what way, why is  this approach wrong, since we know "all models are wrong, but some are useful"?   1. Whittingham, M.J., Stephens, P.A., Bradbury, R.B., &amp; Freckleton, R.P. (2006). Why do we still use stepwise modelling in ecology and behaviour? Journal of Animal Ecology, 75, pp. 1182–1189. Regex matches but shouldn't Inbox chops messages in the middle of an HTML character reference The messages in the inbox get chopped if they too long, and the chop can occur in the middle of an HTML character reference as can be seen in this screenshot:    The character being chopped is [ and it appears inside a code snippet, in case it makes a difference. I'm new to blender and trying to model the blade of my helicopter and can't figure out how to make an edge curved (for the red tip and selected edge). The object is a plane, with one loop cut. I attempted making a bevel Ctrl B, but nothing happens (A dotted line appears attached to the cursor, moving does nothing, left-clicking does nothing).  also I cant add a curve modifier, just says its disabled. What is the correct way to model this? How can I make a script run automatically after gdm login and logout? I have a setup where my users log on using ldap and it works just fine.  I want to run a script after my users login (its a script that will detect which groups they are in and map network shares accordingly), and after they logout (umounting their shares).  Both scripts are done and they work.  I want that when the user logs in the box a script runs downloading the mounting script from my server (wget i guess?) and runs it, same thing for logout.  Can it be done? I've been searching the net and had no luck so far. I've managed to make that work on shell login/logout, but my users dont even know what shell is and have no use for it :) How to find Oracle's installed version and release from a program? What is a terminal? How do I open a terminal window? How do I use the terminal? Negative values for AICc (corrected Akaike Information Criterion) I have calculated AIC and AICc to compare two general linear mixed models; The AICs are positive with model 1 having a lower AIC than model 2.  However, the values for AICc are both negative (model 1 is still &lt; model 2).  Is it valid to use and compare negative AICc values? Why can’t the Doctor’s companions understand babies and horses? The Doctor claimed to speak both horse and baby. The reason human companions can understand every language is because the TARDIS translates. So why can't anyone else understand babies and horses? How to read ND filter description? When I search on Amazon for eg. neutral density 67mm, I get long list of different filters. Some of them are marked like: ND2, ND4, ND8 etc. I'm guessing this means 2-, 4- or 8-stops filter, am I right?  But what about filters, that say 0.6 or 0.9? What does this mean?   Is there any other thing (apart of stops and diameter) that I should also pay attention to when choosing a filter? Is there a hack to force Twitter not to convert words like ASP.NET to links? Currently, Twitter converts anything that has dot inside it into a link, e.g. ASP.NET becomes , Any.DO becomes  etc. I currently make a space if I want the word to stay the way it should, e.g. "ASP. NET" though it is not right.  Is there a hack around this Twitter bug? Like if there would be some unicode character that looked like a dot and could be inserted there or something like that. Determining application path in a Python EXE generated by pyInstaller I have an application that resides in a single .py file.  I've been able to get pyInstaller to bundle it successfully into an EXE for Windows.  The problem is, the application requires a .cfg file that always sits directly beside the application in the same directory.  Normally, I build the path using the following code:  import os config_name = 'myapp.cfg' config_path = os.path.join(sys.path[0], config_name)   However, it seems the sys.path is blank when its called from an EXE generated by pyInstaller.  This same behaviour occurs when you run the python interactive command line and try to fetch sys.path[0].  Is there a more concrete way of getting the path of the currently running application so that I can find files that are relative to it? How can I know if a branch has been already merged into master? I have a git repository with multiple branches.   How can I know which branches are already merged into the master branch? How do I redirect to another webpage? How can I redirect the user from one page to another using jQuery or pure JavaScript? execute drush command from devel/php drupal Can any one please tell me how can I execute drush command from devel/php?  I can execute PHP codes from devel/php. But I don't know how can I execute drush command from devel/php. (As we know "devel/php" URL coming from devel module).  I have written some custom drush command for cron purpose. I can able to run those commands from command line.  &gt; drush my-cmd or drush cc all or drush status , etc ... I can run it through command line.   Expecting some function as mentioned below to run from devel/php  some_function("drush cc all"); Is there to make the login screen appear on the external display in 18.04? On Ubuntu 18.04, I have connected my laptop to an external display and I am able to set the external display as primary and external display only mode. But when I turn on my laptop or log out from my session the display login screen is displayed only on my(internal) laptop screen. But once I login the display switches to external only and my laptop screen turns off as expected. Is there a way I can make the login screen appear only on the external screen on bootup or on logout as in 16.04? Also the login screen does not follow my cursor as in 16.04. Should reputation from SO carry over to Meta? An example of the nucleus of an atom being in an excited state is the , which was a theory devised by the Astronomer Fred Hoyle to help describe the vast quantities of carbon-12 present in the universe, which wouldn't be possible without said Hoyle State.  It's easy to visualise and comprehend the excited states of electrons, because they exist on discrete energy levels that orbit the nucleus, so one can easily see how an electron can excite from one energy level into a higher one, hence making it excited.  However, I can't see how the nucleus can get into an excited state, because clearly, they don't exist on energy levels that they can transfer between, but instead it's just a 'ball' of protons and neutrons.  So how can the nucleus of an atom be excited? What makes it excited?