structure for 'Theory of Logic'    |     alphabetical list of themes    |     expand these ideas

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

[general features of logical models]

35 ideas
We can show that a concept is consistent by producing something which falls under it [Frege]
A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach]
Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
Models in model theory are structures, not sets of descriptions [Hodges,W]
A model is 'fundamental' if it contains only concrete entities [Jubien]
Model theory is unusual in restricting the range of the quantifiers [Field,H]
Model theory studies how set theory can model sets of sentences [Hart,WD]
Model theory is mostly confined to first-order theories [Hart,WD]
Models are ways the world might be from a first-order point of view [Hart,WD]
Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
Semantics for models uses set-theory [Shapiro]
Model theory deals with relations, reference and extensions [Shapiro]
The central notion of model theory is the relation of 'satisfaction' [Shapiro]
We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
Models leave out meaning, and just focus on truth values [Burgess]
We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
If every model that makes premises true also makes conclusion true, the argument is valid [Melia]
Sentence logic maps truth values; predicate logic maps objects and sets [Merricks]
A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
Model theory reveals the structures of mathematics [Wolf,RS]
Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
First-order model theory rests on completeness, compactness, and the L÷wenheim-Skolem-Tarski theorem [Wolf,RS]
Permutation Theorem: any theory with a decent model has lots of models [Button]
A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]