Model-theoretic validity refers to the truth of a statement within all possible interpretations or models. It's a cornerstone of formal…
Model-theoretic consequence is a fundamental concept in logic, defining logical implication through the interpretation of formulas in models. It ensures…
A model in logic and mathematics interprets the symbols of a formal language, satisfying the axioms and theorems of a…
Metatheory involves the theoretical analysis of mathematical and logical systems. It examines properties, structure, and foundational aspects, providing a meta-level…
A maximal consistent set is a collection of logical formulas that is both consistent and cannot be extended further without…
A fundamental theorem in mathematical logic stating that any countable theory with an infinite model has models of all infinite…
A theorem stating that if A implies B is provable, a formula C exists using only common symbols. Both A…
Henkin semantics offers a flexible alternative to standard first-order semantics, allowing quantifiers to range over restricted domains within models. This…
Finite model theory explores structures with finite domains. It investigates properties and expressiveness of logical languages within these finite settings,…
Elementary equivalence signifies that two structures share all the same first-order sentences. This concept is crucial in model theory for…