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The model-theory tag has no summary.
19 questions
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What does it mean for a domain of discourse to exist?
The following sentences seem true:
For all X1, if X1 is a theory then X1 is consistent if and only if there doesn’t exist X2 such that X2 is an element of X1 and X2 contradicts any element of X1.
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3
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321
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Is this an easy way to prove that all five postulates of Euclidean Geometry are consistent?
Is this an easy way to prove that all five postulates of Euclidean Geometry are consistent?
I ask because of the following. In order to prove that a theory is consistent, there must exists a model or ...
- 1,346
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1
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121
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Similarities Between Category Theory, Model Theory, FOL, and HOL [closed]
Is Category Theory analogous to a mixture of Model Theory, First Order Logic, and Higher Order Logic in sheep's clothing? I ask because of the following.
Let us consider the definition of ...
- 1,346
4
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2
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401
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Ambiguity on the definition of a model in model theory
Is the following definition of a model in model theory ambiguous? The definition is the following: A model of a theory is an interpretation of the theory that makes all sentences in the theory true. I ...
- 1,346
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77
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Does the Loewenheim-Skolem Theorem apply to the Metaphysical System of St. Thomas Aquinas?
Does the Loewenheim-Skolem Theorem apply to the Metaphysical System of St. Thomas Aquinas? I ask because of the following:
Let us consider the metaphysical system of St. Thomas Aquinas as devoid of ...
- 1,346
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2
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84
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Interpreting a sentence in mathematics
Consider the following sentence, For all X1, X1 is a prime number if and only if for all X2, if X2 divides X1, then X2 equals one or X2 equals X1. What kind of interpretations and how many ...
- 1,346
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3
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99
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Can you treat any scientific theory as a deductive theory where all sentences lack meaning and assign different interpretations to them?
Can you treat any scientific theory as a deductive theory where all the sentences in the theory are devoid of meaning and then assign different interpretations to them? I ask because Russell did that ...
- 1,346
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6
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925
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What's the difference between a theory and a model (i.e. structure) of the theory?
What's the difference between a theory and a model (i.e. structure) of the theory? I ask because it seems that there's no difference between the two and that a theory can be considered a model of ...
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7
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1
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170
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How to understand interpretation in plurality-basis model theory
I am reading Linnebo & Florio's book The many and the one (2021) at ch.7.
Here, Linnebo attempts to contrast between set-based model theory on plural logic and plurality-based model theory.
For ...
- 479
2
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1
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149
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How would you adapt modern day model-theoretic formal semantics, to allow for usual/unusual meanings? [closed]
In language , we can employ usual meanings of language-tokens and unusual meaning of language-tokens
without the notion of "usual meaning" of language-tokens, communication would be a ...
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Can we think of model theoretical interpretation as an ontological commitment?
I think there is a relationship between model theory and ontological commitments, particularly how the model-theoretic consequence relation (|=) might be viewed as a form of ontological commitment. ...
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93
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What kinds of entities typically exist in the domain of a first-order language?
I am reading the Wikipedia page on nonfirstorderizability.
It mentions the Kaplan sentence as a paradigm of this concept, explaining that there cannot exist a formula in the first-order language of ...
- 479
4
votes
3
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468
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Compactness Theorem for propositional Calculus
The compactness Theorem of PC says that a possibly infinite Set of Propositional Formulas, Γ, has a Model if and only if all its Finite Subsets have a Model.
I assume that we can understand a Model as ...
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3
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233
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How can we prove that PA has a model?
I have read that Con(PA) can be proved within ZFC (I would guess, by explicitly constructing a model of PA.) But I have also read that we do not know whether ZFC has a model or not. So, if Con(ZFC) ...
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4
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512
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Framework for explaining the notion "implementing according to a specification"?
Explaining "Implementing a specification"
I'm currently looking into the notion of "implementing according to a specification" in engineering, and in particular in software ...
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