特殊篇章玄宇宙计划原文序列部分章 (5-1)

介绍：特殊篇章玄宇宙计划原文分为（4/5）篇的章节。

THE HYTERUNIVERSE FROGRAM 91

if it is ablc to describe what can be true in alternative universes, A precisc

criterion based upon this principle is the following.

CRITERION OF OMNISCIENCE, Let Φ be the set of sentences with arbitrary

parameters from ∪ which can hold in some outer model of ∪ e. Then Φ is

first-order definable in ∪.

This kind of statement first appeared in unpublished work of Mack Stan-

ley, where he shows that there are omniscient universes (in our terminology). assuming a bit less than the consistency of a measurable cardinal (stationary-many Ramsey cardinals, roughly speaking). One may be tempted to regard omniscicnce as a form of power set maximality; this is unlikely, however, for whereas power-set maximality does not allow any parameters,the principle

of omniscience allows arbitrary set parameters.

Synthesizing ordinal maximality with omniscience should not be diflicult.

using indiscernibles for the Dodd-Jensen core model in the presence of Ramsey cardinals. An intriguing open question is how to achieve a grander synthesis with power set maximality. The obvious approach, asserting power set maximality for omniscient and ordinal maximal universes, appears to be

inconsistent. It is nevertheless reasonable to conjecture that some such grand

synthesis is possible. but its formulation will be subtle and the mathematics

required to verify consistency may be challenging.

数学联邦政治世界观提示您：看后求收藏（同人小说网http://tongren.me），接着再看更方便。