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Single Idea 13532
[filed under theme 5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
]
Full Idea
A 'structure' in model theory has a non-empty set, the 'universe', as domain of variables, a subset for each 'relation', some 'functions', and 'constants'.
Gist of Idea
Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants'
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.2)
Book Ref
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.167
The
35 ideas
with the same theme
[general features of logical models]:
22294
|
We can show that a concept is consistent by producing something which falls under it
[Frege]
|
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
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A 'model' is a meaning-assignment which makes all the axioms true
[George/Velleman]
|
5741
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If every model that makes premises true also makes conclusion true, the argument is valid
[Melia]
|
19207
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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
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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]
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