New posts in first-order-logic

Proving $\forall x[p\vee\Phi(x)]\Longleftrightarrow [p\vee\forall x[\Phi(x)]$, where $p$ does not contain $x$ as a free variable

logic first-order-logic predicate-logic quantifiers

When do free variables occur? Why allow them? What is the intuition behind them?

logic predicate-logic first-order-logic

Understanding the meaning of $\forall,\exists$ rules in sequent calculus.

logic first-order-logic quantifiers proof-theory sequent-calculus

Trying to understand Sequent Calculus inference rules for quantifiers $\forall$ and $\exists$.

first-order-logic quantifiers sequent-calculus

Need help regarding a proof in First Order Logic

logic propositional-calculus first-order-logic

In first order logic, is $(\text{True}\lor P(x))$ considered $\text{True}$ (where the variable $x$ is free)?

logic first-order-logic

Strong Induction Requires No Base Case?

induction first-order-logic

In what sense is propositional logic "zeroth-order logic?"

logic propositional-calculus predicate-logic first-order-logic

How is first-order logic a strong enough logic for the foundations of mathematics?

logic set-theory definition first-order-logic foundations

In Tarskian semantics, can we assign a name to every object, in every model of every first order theory?

logic first-order-logic model-theory

Completeness and Incompleteness

logic predicate-logic first-order-logic

What is the operator precedence for quantifiers?

first-order-logic

Need help to write a proof regarding first order formula

propositional-calculus first-order-logic formal-languages computational-mathematics

About Gödel-Gentzen negative translation

first-order-logic constructive-mathematics intuitionistic-logic

Kees Doets's definitions of logical consequence

logic first-order-logic predicate-logic model-theory satisfiability

What is wrong with this naive approach to Hilbert's 10th problem?

number-theory proof-verification logic first-order-logic decidability

Is there a Second-Order Axiomatization of ZF(C) which is categorical?

logic set-theory model-theory foundations first-order-logic

What is the so-called eigenvariable or parameter in natural deduction?

logic first-order-logic quantifiers proof-theory natural-deduction

Equivalent categories are elementarily equivalent: Formalization?

category-theory predicate-logic first-order-logic

Can we express the theory of a single topology as a multi-sorted theory?

general-topology first-order-logic