特殊篇章玄宇宙计划原文序列部分章 (12-12)

such statements are the following (see [7].[8].[1]):

1. There are small large cardinals and inner models with measurable car-

dinals of arbitrary Mitchell order.

2. For some real R. R# does not exist and so Jensen covering holds with

respect to L[R],the constructible universe relativised to R.As a result:

3.There are no measurable cardinals, the singular cardinal hypothesis is

truc, the continuum is not real-valued measurable,projective deter-

minacy (PD) is false, the proper forcing axiom is false and there are

non-Borel analytic sets which are not Borel isomorphic.

The Contiman Hypothesis remains undecided, cven assuming that there

exists a universe that obeys the Synthesis Conjecture.One needs a stronger

version of power set maximality than the Inner Model Hypothesis to settle

CH. i.e,the hypothesis for formulas with globally absolute parameters.¹⁵ A

consistency proof for the resulting Strong Inner Model Hypothesis(SIMH)

is however still lacking.

Omniscience and a Grander Synthesis? Yet another source of criteria for

preferred universes is the principle of omniscience A universe is omniscient

＿＿＿＿＿＿

¹⁵See [8].

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