Ambiguity and stratification

Crabbé, Marcel

doi:10.4064/fm-101-1-11-17

Cited by 10 publications

(6 citation statements)

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“…Connecting to the paragraph preceding the axiomatization, every stratified theorem of NF has a stratified proof [Crabbé, 1978].…”

Section: Stratified Set Theorymentioning

confidence: 99%

Self-similarity in the Foundations

Gorbow¹

2019

Bull. symb. log

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Let M, N be L-structures. M is a substructure of N if M ⊆ N and for every constant symbol c, relation symbol R and function symbol f of L, we haveNote that since M is an L-structure, the condition on function symbols implies that M, as a subset of N , is closed under f N . We also say that N is an extension of M. The substructure is proper if its domain is a proper subset of the domain of the extension, in which case we write M < N . Note that M ≤ N ⇔ M < N ∨ M = N , whence this defines a partial order.If a subset S of N is closed under the interpretation of all constant and function symbols of N , then we have a substructure N ↾ S of N , called the restriction of N to S, on the domain S defined by c N ↾ S = c N , R N ↾ S = R N ∩ S arity(R) and f N ↾ S = f N ∩ S arity(f )+1 , for all constant, relation and function symbols, c, R, f , respectively.An embedding f : M → N from an L-structure M to an L-structure N is a function f : M → N , such that for each atomic L-formula φ( x) and for each m ∈ M, we have

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“…Connecting to the paragraph preceding the axiomatization, every stratified theorem of NF has a stratified proof [Crabbé, 1978].…”

Section: Stratified Set Theorymentioning

confidence: 99%

Self-similarity in the Foundations

Gorbow¹

2019

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“…Ifa is an LCTT-sentence, let a + denote the AaTT-sentence obtained by adding I to all type superscripts in a. Classically (see [3]), it can be proved that {trr a + : a is an 5r…”

Section: Intuitionistic Ambiguity Versus Classical Ambiguitymentioning

confidence: 99%

“…For example, [3] remarks that s can be replaced by some other languages, while [7] extends the definition of "ambiguous structure". -What are the properties of cardinals and ordinals in intuitonistic TT or NF (including the right way to define them, the axiom of infinity and the axiom of choice)?…”

Section: Open Problemsmentioning

confidence: 99%

Intuitionistic typical ambiguity

Dzierzgowski

1992

Arch Math Logic

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“…We also find such formulas in the system PT, this theory is an extension of Peano Arithmetic introduced by E. Specker and its models are exactly the models of Peano Arithmetic where a new 1-placed function symbol is interpreted by any automorphism of the structure. In [4], M. Crabbe considers stratified formulas for a first-order language which includes some relation symbols. The stratified formulas considered here are similar to the latter; yet we allow the language to contain not only function symbols (which add nothing new) but also constants.…”

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confidence: 99%

Stratified languages

Pétry

1992

J. symb. log.

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We consider arbitrary stratified languages. We study structures which satisfy the same stratified sentences and we obtain an extension of Keisler's Isomorphism Theorem to this situation. Then we consider operations which are definable by a stratified formula and modify the ‘type’ of their argument by one; we prove that for such an operation F the sentence c = F(c) and the scheme φ(c) ↔ (F(c)), where ↔(x) varies among all the stratified formulas with no variable other than x free, imply the same stratified {c}-sentences.

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Ambiguity and stratification

Cited by 10 publications

References 0 publications

Self-similarity in the Foundations

Self-similarity in the Foundations

Intuitionistic typical ambiguity

Stratified languages

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