New posts in first-order-logic

Soundness multiple definitions

logic first-order-logic

Looking for help in understanding a proof of the fixed point lemma in mathematical logic.

logic first-order-logic predicate-logic fixed-point-theorems

Why can't we formalize the lambda calculus in first order logic?

logic first-order-logic lambda-calculus combinatory-logic

Is $\Bbb R$ definable in $(\Bbb C,0,1,+,*,\exp)$?

logic model-theory first-order-logic

Predicate vs function [duplicate]

logic first-order-logic

is there a short, unambiguous way to write that a statement isnt always true?

logic first-order-logic

With this definition of completeness, Gödel's Incompleteness result seems not surprising, so why it was back then?

logic first-order-logic incompleteness

Running an infinite amount of Turing Machine steps in a finite amount of time: What consequences?

logic set-theory first-order-logic computability turing-machines

Given ∃x.¬p(x), use the Fitch System to prove ¬∀x.p(x).

logic predicate-logic first-order-logic natural-deduction formal-proofs

Do we have to prove how parentheses work in the Peano axioms?

logic definition first-order-logic axioms peano-axioms

How to think about theories that prove their own inconsistency?

logic soft-question first-order-logic philosophy

Established conventions for distinguishing the consequence relations of FOL

logic notation soft-question terminology first-order-logic

How does Gödel Completeness fail in second-order logic?

logic model-theory first-order-logic incompleteness nonstandard-models

Is the compactness theorem (from mathematical logic) equivalent to the Axiom of Choice?

model-theory axiom-of-choice first-order-logic

What is the purpose of free variables in first order logic?

logic first-order-logic

Set theoretic concepts in first order logic

logic first-order-logic philosophy

Is there a decision procedure for *monadic* intuitionist first-order logic?

logic first-order-logic constructive-mathematics intuitionistic-logic

Are the natural numbers implicit in the construction of first-order logic? If so, why is this acceptable?

logic set-theory first-order-logic

Is $ \pi $ definable in $(\Bbb R,0,1,+,×, <,\exp) $?

real-analysis model-theory first-order-logic

What's the problem in logic in defining satisfaction in terms of a formal translation (and thus obtain the rules as theorems)?

logic first-order-logic