axiom schema of predicative separation, or of restricted, or Δ0 separation, is a schema of axioms which is a restriction of the usual axiom schema of...

an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage of an axiomatic...

Intersection (which is related to the Axiom schema of predicative separation) and the Set Induction schema. Taken as axioms, the aforementioned principles constitute...

particular, in the axiom schema of predicative separation only sentences with set bound quantifiers may be used. The restricted form of excluded middle provable...

the axiom schema of replacement with that of separation; General set theory, a small fragment of Zermelo set theory sufficient for the Peano axioms and...

containing precisely those elements x for which φ(x) holds. (This is an axiom schema.) Axiom of Δ0-collection: Given any Δ0 formula φ(x, y), if for every set x...

difference between predicative and non-predicative functions, so they introduced the axiom of reducibility, saying that for every non-predicative function there...

replacing the axiom schema of comprehension with the much weaker axiom schema of separation. However, this step alone takes one to theories of sets which...

set Axiom schema of predicative separation Axiom of separation for formulas whose quantifiers are bounded Axiom schema of replacement The image of a set...

it gives the axiom of separation with P {\displaystyle P} . Mancini, Antonella; Montagna, Franco (Spring 1994). "A minimal predicative set theory". Notre...

variables in NBG's axiom schema of Class Comprehension are restricted to sets; hence Class Comprehension in NBG must be predicative. (Separation with respect...

φz^. The axiom of reducibility states that any truth function (i.e. propositional function) can be expressed by a formally equivalent predicative truth function...

theories suffice: They shall adopt the Axiom of infinity, the Axiom schema of predicative separation to prove induction of arithmetical formulas in ω {\displaystyle...

program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described...

non-existence of a set of all sets also already follows from Predicative Separation. In a set theory, theories of mathematics are modeled. Weaker logical axioms mean...

axiom schema to imply nonprojectibility, in fact there are transitive models of K P {\displaystyle KP} + Σ 1 {\displaystyle \Sigma _{1}} -separation of...