Elementary equivalence signifies that two structures share all the same first-order sentences. This concept is crucial in model theory for…
An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…
The downward Löwenheim–Skolem theorem states that if a theory has an infinite model, it has a model of every infinite…
The disjunction property in intuitionistic logic asserts that if a statement P or Q is provable, then either P alone…
A crucial lemma in Gödel's incompleteness theorems. It states that for any formula with one free variable, there exists a…
A conservative extension adds new axioms or rules to a theory without altering the truth of existing statements. This ensures…
The comprehension schema is a fundamental principle in set theory and logic. It allows for the construction of sets by…
A fundamental theorem in mathematical logic asserting that if every finite subset of a set of sentences is satisfiable, then…
Combinatory logic is a branch of mathematical logic that aims to simplify mathematical expressions by replacing variables with combinators. It…
Categorical logic, rooted in category theory, explores object categorization and the logical underpinnings of categories. It provides a formal framework…