2 Übersetzungen
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- Kelley-Morse-Mengenlehre {f} [selten] [Morse-Kelley-Mengenlehre] = Kelley-Morse set theory <KM set theory>
- Morse-Kelley-Mengenlehre {f} <MK-Mengenlehre> = Morse-Kelley set theory <MK set theory>
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- The picture of the universe of sets stratified into the cumulative hierarchy is characteristic of ZFC and related axiomatic set theories such as Von Neumann–Bernays–Gödel set theory (often called NBG) and Morse–Kelley set theory.
- Solovay has shown the precise equivalence in consistency strength of NFUB = NFU + "Infinity" + "Cantorian Sets" + "Small Ordinals" with Morse–Kelley set theory plus the assertion that the proper class ordinal (the class of all ordinals) is a weakly compact cardinal.
- In class theories such as Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, there is an axiom called the axiom of global choice that is stronger than the axiom of choice for sets because it also applies to proper classes.
- Morse–Kelley set theory (MK) allows classes to be defined by formulas whose quantifiers range over classes.
- Morse–Kelley set theory admits proper classes as basic objects, like NBG, but also allows quantification over all proper classes in its class existence axioms.
- Kunen used Morse–Kelley set theory in his proof. If the proof is re-written to use ZFC, then one must add the assumption that replacement holds for formulas involving "j".
- These classes can serve as inner models for various axiomatic systems such as ZFC or Morse–Kelley set theory.
- Kelley's 1955 text, "General Topology", which eventually appeared in three editions and several translations, is a classic and widely cited graduate-level introduction to topology.
© dict.cc English-German dictionary 2024
Enthält Übersetzungen von der TU Chemnitz sowie aus Mr Honey's Business Dictionary (nur Englisch/Deutsch).
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