Prove that a theory $\Gamma$ is consistent if and only if there is a structure $M$ so that $M$ $\models$ $\Gamma$.
139278
If $\Gamma$ is satisfiable then $\Gamma$ is consistent
111165
Prove the converse of Wilson's Theorem
128111
Why is a deductive closure an intersection of maximally consistent sets?
91698
Proofs of consistency for two formal systems
132532
Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
99376
Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.
19604
Complete first order theory with finite model is categorical
31389
consistency of ZF\{Power Set axiom}
88188
Explain proof by contradiction.
120065
Niven’s theorem proof.
91281
Proving the so-called "Well Ordering Principle"
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
12449
How to formulate continuum hypothesis without the axiom of choice?
136613
Does TG prove that ZFC2 has a model?
31392
Examples and Counterexamples of Relations which Satisfy Certain Properties
115224
Equivalences of $\diamondsuit$-principle.