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

#### [general features of logical models]

34 ideas
 13343 A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski]
 16323 The object language/ metalanguage distinction is the basis of model theory [Tarski, by Halbach]
 13826 Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
 10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
 10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
 10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
 9968 A model is 'fundamental' if it contains only concrete entities [Jubien]
 10827 Model theory is unusual in restricting the range of the quantifiers [Field,H]
 13505 Model theory studies how set theory can model sets of sentences [Hart,WD]
 13511 Model theory is mostly confined to first-order theories [Hart,WD]
 13512 Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
 13513 Models are ways the world might be from a first-order point of view [Hart,WD]
 13644 Semantics for models uses set-theory [Shapiro]
 10240 Model theory deals with relations, reference and extensions [Shapiro]
 10239 The central notion of model theory is the relation of 'satisfaction' [Shapiro]
 15411 We only need to study mathematical models, since all other models are isomorphic to these [Burgess]
 15412 Models leave out meaning, and just focus on truth values [Burgess]
 15416 We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess]
 10903 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]
 13724 In model theory, first define truth, then validity as truth in all models, and consequence as truth-preservation [Sider]
 10129 A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
 5741 If every model that makes premises true also makes conclusion true, the argument is valid [Melia]
 19207 Sentence logic maps truth values; predicate logic maps objects and sets [Merricks]
 10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
 10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
 10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
 13519 Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
 13531 Model theory reveals the structures of mathematics [Wolf,RS]
 13532 Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
 13533 First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS]
 18694 Permutation Theorem: any theory with a decent model has lots of models [Button]
 10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
 18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
 17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]