# Tagged Questions

Questions about mathematical logic, including model theory, proof theory, computability theory (a.k.a. recursion theory), and non-standard logics. Questions which merely seek to apply logical or formal reasoning to other areas of mathematics should not use this tag. Consider using one of the ...

47 views

### If empty set is a subset of empty set is always true , then is empty set not a subset of empty set always false? [closed]

If $\varnothing \subseteq \varnothing$ is always true , is $\varnothing \subsetneq \varnothing$ always false ? Any proofs ?
47 views

### What are the different ways to get a first-order formula that express the statement“$P$ is the $n$-th prime”

I know that such a $2$-predicate formula exists since Enderton's have already constructed such a formula in his text on mathematical logic but it was not easy to remember so I wonder if there is other ...
23 views

### Predicate calculus -help [duplicate]

I need to prove that the ∃x(R(x)→∀yR(y)) is logically valid. I'm trying to understand why this statement is true but I can't figure it out.
54 views

### What is the intutition behind the negative exponential ? in linear logic?

The positive exponential ! has a very satisfying interpretation in terms of the standard resource interpretation of linear logic. Given a resource $a$, we know that $!a$ means an infinite supply of $a$...
37 views

68 views

### Is this symbolic statement impossible?

Is this statement logically impossible if x is a single real number (i.e. not a set)? $$(x<5) \land(x>7)$$ it seems to me that x cannot both be greater than 7 and less than 5 if ...
26 views

58 views

### Adding witnesses to prove Gödel's completeness theorem

I am currently working with "The Foundations of Mathematics" by Kunen to understand the proof for Gödel's completeness theorem due to Henkin. When adding the witnessing terms, there is one thing I ...
111 views