Non-Standard Models in Logic and Mathematics
A non-standard model adheres to a theory's axioms but possesses unintended properties.…
Neo-Logicism in the Philosophy of Mathematics
Neo-logicism revives the logicist project of grounding mathematics in logic. It addresses…
Neo-Fregeanism: A Modern Approach to Logicism
Neo-Fregeanism revives Frege's logicist project, aiming to base mathematics on logic. It…
Model-Theoretic Validity
Model-theoretic validity refers to the truth of a statement within all possible…
Metamathematics
Metamathematics examines mathematical systems and theories from an elevated viewpoint, employing principles…
Mathematical Logic
Mathematical logic is the study of logic within mathematical reasoning. It explores…
Material Biconditional: Understanding the “If and Only If”
The material biconditional, or "if and only if" (iff), is a logical…
Löwenheim–Skolem Theorem
A fundamental theorem in mathematical logic stating that any countable theory with…