Standard models of set theory with predication

Standard Models of Set Theory with Predication

The Interpretation of Set Theory in Mathematical Predication Theory

Rumfitt’s Theory of Predication∗

Before Frege there was no satisfactory way of explaining both the validity of the inference of (B) from (A) and also that of the inference of (C) from (B). Frege’s solution has several components, but one key element is his ability to decompose (B) in at least two different ways. The unasserted proposition contained in (B) can be seen as obtained by attaching the expression of generality ‘someb...

Models of Set Theory

1. First order logic and the axioms of set theory 2 1.1. Syntax 2 1.2. Semantics 2 1.3. Completeness, compactness and consistency 3 1.4. Foundations of mathematics and the incompleteness theorems 3 1.5. The axioms 4 2. Review of basic set theory 5 2.1. Classes 5 2.2. Well-founded relations and recursion 5 2.3. Ordinals, cardinals and arithmetic 6 3. The consistency of the Axiom of Foundation 8 ...

Models of set theory with definable ordinals

A DO model (here also referred to a Paris model) is a model M of set theory all of whose ordinals are first order definable in M. Jeffrey Paris (1973) initiated the study of DO models and showed that (1) every consistent extension T of ZF has a DO model, and (2) for complete extensions T, T has a unique DO model up to isomorphism iff T proves V = OD. Here we provide a comprehensive treatment of...