scholarly journals A Note on Indestructibility and Strong Compactness

2008 ◽  
Vol 56 (3-4) ◽  
pp. 191-197
Author(s):  
Arthur W. Apter
Keyword(s):  
Strong Compactness

Level by level equivalence and strong compactness

2003 ◽  
Vol 50 (1) ◽  
pp. 51-64
Author(s):  
Arthur W. Apter
Keyword(s):  
Strong Compactness

Measurability and degrees of strong compactness

1981 ◽  
Vol 46 (2) ◽  
pp. 249-254 ◽  
Author(s):  
Arthur W. Apter
Keyword(s):  
Large Degree ◽  
Strong Compactness ◽  
Measurable Cardinals ◽  
Relationship Of ◽  
The Relationship

AbstractWe prove, relative to suitable hypotheses, that it is consistent for there to be unboundedly many measurable cardinals each of which possesses a large degree of strong compactness, and that it is consistent to assume that the least measurable is partially strongly compact and that the second measurable is strongly compact. These results partially answer questions of Magidor on the relationship of strong compactness to measurability.

scholarly journals Fuzzifying Strongly Compact Spaces and Fuzzifying Locally Strongly Compact Spaces

2017 ◽  
Author(s):  
O. R. Sayed ◽  
Adem Kiliҫman
Keyword(s):  
Compact Spaces ◽  
Strong Compactness

In this paper, some characterizations of fuzzifying strong compactness are given, including characterizations in terms of nets and pre -subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

scholarly journals Relative consistency results via strong compactness

1991 ◽  
Vol 139 (2) ◽  
pp. 133-149 ◽  
Author(s):  
Arthur Apter ◽  
James Henle
Keyword(s):  
Relative Consistency ◽  
Strong Compactness ◽  
Consistency Results

scholarly journals WOODIN FOR STRONG COMPACTNESS CARDINALS

2019 ◽  
Vol 84 (1) ◽  
pp. 301-319
Author(s):  
STAMATIS DIMOPOULOS
Keyword(s):  
Identity Crisis ◽  
Large Cardinal ◽  
Strongly Compact Cardinal ◽  
Compact Cardinal ◽  
Strong Compactness ◽  
Definition Of ◽  
Vopěnka Cardinals

AbstractWoodin and Vopěnka cardinals are established notions in the large cardinal hierarchy and it is known that Vopěnka cardinals are the Woodin analogue for supercompactness. Here we give the definition of Woodin for strong compactness cardinals, the Woodinised version of strong compactness, and we prove an analogue of Magidor’s identity crisis theorem for the first strongly compact cardinal.

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