Gch implies weakly strongly inaccessible
Webinaccessible cardinal, and 2 D C if is a measurable cardinal. Further, in VP, for every pair of regular cardinals < , is -strongly compact if and only if is -supercompact, except possibly … WebJan 22, 2024 · $\begingroup$ If you only have one inaccessible cardinal, add $\kappa^+$ Cohen reals, then it is weakly inaccessible, and you cannot force back GCH while …
Gch implies weakly strongly inaccessible
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http://faculty.baruch.cuny.edu/aapter/papers/lev12b.pdf Web$\begingroup$ I think the statement, "There are no inaccessibles" is a large powerset axiom already: it asserts that, for every uncountable regular $\kappa$, there is some $\lambda<\kappa$ such that $2^\lambda\ge\kappa$; and we can make this even stronger by adding "$\mu<\nu\implies 2^\mu<2^\nu$, to demand a $\lambda<\kappa$ with …
WebFeb 10, 2024 · PDF We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal $\lambda$ for which the sequence $\langle 2^\theta:\theta Find, read and cite all the research you ... WebMar 29, 2024 · The result is useful especially under the failure of GCH, since GCH implies that \(2^{\aleph _1}=\aleph _2\). In addition, it is an easy application of Shoenfield’s absoluteness that \(\aleph _0\) -amalgamation is an absolute property for models of ZFC.
WebMar 18, 2024 · Silver [5, Theorem 5.8] has shown that the consistency of ZFC + “there is a weakly compact cardinal” implies the consistency of ZFC + not GCH + “there is no ω 2 -Aronszajn tree, hence no ω ... WebJan 31, 2024 · Silver [5, Theorem 5.8] has shown that the consistency of ZFC + “there is a weakly compact cardinal” implies the consistency of ZFC + not GCH + “there is no ω 2 -Aronszajn tree, hence no ω ...
WebFeb 9, 2024 · We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal $$\\lambda$$ λ for which the sequence $$\\langle 2^\\theta:\\theta<\\lambda\\rangle$$ 2 θ : θ < λ is not eventually constant and the weak diamond fails at $$\\lambda$$ λ . We also prove that consistently diamond fails but a …
WebApr 30, 2024 · Specifically: (a) It is proved in [13] that if ω 2 is not weakly compact in L, then either ω 1 holds or there is a non-special ℵ 2 -Aronszajn tree; in particular, GCH+SATP ℵ 2 implies that ... gravel in checotah okWebEnter the email address you signed up with and we'll email you a reset link. graveline bay marsh restorationWebSTRONGLY ALMOST DISJOINT SETS AND WEAKLY UNIFORM BASES 3 If cf(δ) ≥ τ, then [I] chmm recertificationWebI asked here about "large powerset axioms" and to my delight, learned that such axioms are being taken seriously. I've been toying with them ever since. My favourite is: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible," since this is easy to understand yet implies the … gravel in chilliwackWebNov 25, 2024 · CH’s argument about heat death of the universe. – duration of design is irrelevant to whether something was designed. – cars are designed, yet they break … graveline bay marsh restoration projectWebstrongly inaccessible numbers (if granted AC). Levy proves [2, p. 228 ] that (1) is equivalent to the conjunction of (2) with the statement "there exist arbitrarily large inaccessible num-bers". As the axiom of choice implies that "strongly inaccessible" and "inaccessible" are the same thing [2, p. 226] it is a consequence of chmm passing scorehttp://math.bu.edu/people/aki/21.pdf chmm pass rate