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Page 2736 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
The author then shows that Pz has the «**-cc, that it looks lo- cally (that is, in the sense of <p) like Radin forcing, that this local part has the «*-cc, and that P} satisfies Prikry’s condition (which  ...  We also make some general remarks and comments.” 2004d:03108 03E40 03E35 03E55 Merimovich, Carmi Extender-based Radin forcing. (English summary) Trans. Amer. Math.  ... 

Page 2117 of Mathematical Reviews Vol. , Issue 84f [page]

1984 Mathematical Reviews  
Radin and W. H. Woodin.  ...  This is reviewed in Section 2 of the present paper, and corresponds to a forcing used by M. Magidor [Fund. Math. 99 (1978), 61-71; MR 57 #5754].  ... 

On the Splitting Number at Regular Cardinals [article]

Omer Ben-Neria, Moti Gitik
2015 arXiv   pre-print
We construct a generic extension with s(κ) = λ starting from a ground model in which o(κ) = λ and prove that assuming 0^, s(κ) = λ implies that o(κ) ≥λ in the core model.  ...  Acknowledgements: The authors are grateful to Ralf Schindler and the referee, for pointing out several errors in an earlier version of this paper. The second author would like to thank J.  ...  The authors believe to have found a modification of the forcing argument in Section 2 which shows that the consistency strength is not greater than o(κ) = κ +ω+1 , however it is not clear whether this  ... 
arXiv:1408.2839v2 fatcat:5kibxiqrmzadbowutjfqcujoae

Restrictions on forcings that change cofinalities

Yair Hayut, Asaf Karagila
2015 Archive for Mathematical Logic  
We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some "damage" to the structure of cardinals and stationary sets.  ...  As a consequence there is no analogue to the Prikry forcing, in terms of "nice" properties, when changing cofinalities to be uncountable.  ...  Therefore properties like distributivity and chain conditions are inherited from Q to P. (4) Every weakly homogeneous forcing is amalgamable. (5) Radin forcing is amalgamable, although not weakly homogeneous  ... 
doi:10.1007/s00153-015-0454-7 fatcat:phczjjnt4ffmjolwembtuvtsdi

ON THE SPLITTING NUMBER AT REGULAR CARDINALS

OMER BEN-NERIA, MOTI GITIK
2015 Journal of Symbolic Logic (JSL)  
We construct a generic extension with s(κ) = λ starting from a ground model in which o(κ) = λ and prove that assuming ¬0¶, s(κ) = λ implies that o(κ) ≥ λ in the core model.  ...  Acknowledgements: The authors are grateful to Ralf Schindler and the referee, for pointing out several errors in an earlier version of this paper. The second author would like to thank J.  ...  The authors believe they have found a modification of the forcing argument in Section 2 which shows that the consistency strength is not greater than o(κ) = κ +ω+1 , however it is not clear whether this  ... 
doi:10.1017/jsl.2015.22 fatcat:rg2b4upgp5hb3psm3arw7dzyja

A Gitik iteration with nearly Easton factoring

William J. Mitchell
2003 Journal of Symbolic Logic (JSL)  
Unlike the forcing used by Gitik, the iterated forcing ℛ λ+1 used in this paper has the property that if λ is a cardinal less then κ then ℛ λ+1 can be factored in V as ℛ κ+1 = ℛ λ+1 × ℛ λ+1,κ where ∣ℛ  ...  λ+1∣ ≤ λ + and ℛ λ+1,κ does not add any new subsets of λ.  ...  If we ignore the final coordinate f then it can be described as follows: first force as described above to obtain a filter F ⊃ U(λ), and then use this filter in a forcing like that of Prikry and Magidor  ... 
doi:10.2178/jsl/1052669060 fatcat:ctykysh5vbg3lhrjm4bolkbney

Radin forcing and its iterations

John Krueger
2007 Archive for Mathematical Logic  
This version of Radin forcing includes as special cases the Prikry forcing and Magidor forcing, both the measurable and supercompact versions.  ...  We provide an exposition of supercompact Radin forcing and present several methods for iterating Radin forcing.  ...  We would like to add a Radin club to P α λ α for each α in A.  ... 
doi:10.1007/s00153-007-0041-7 fatcat:rhxihmyglzcznlgmpdkedjf4ye

Intermediate Models in Magidor-Radin Forcing- Part I [article]

Tom Benhamou, Moti Gitik
2022 arXiv   pre-print
We prove that for every set A in a Magidor-Radin generic extension using a coherent sequence such that o^U⃗(κ)<κ, there is a subset C' of the Magidor club such that V[A]=V[C'].  ...  We continue the work done by Gitik, Kanovei, Koepke, and later by the authors.  ...  The authors would like to thank the referee for his careful examination of the paper and for many useful insights.  ... 
arXiv:2009.12775v3 fatcat:5t36w2vovndexe5vu3dfa4geli

Page 2783 of Mathematical Reviews Vol. , Issue 88f [page]

1988 Mathematical Reviews  
2783 izes, provided Prikry forcing is replaced by a generalization of it due to Magidor; moreover, he shows that in this case Magidor forcing is equivalent to another generalization of Prikry forcing due  ...  to Radin.  ... 

Extender Based Radin Forcing [article]

Carmi Merimovich
2000 arXiv   pre-print
This forcing satisfies Prikry like condition, destroys no cardinals, and has a kind of properness.  ...  We define extender sequences, generelizing measure sequences from Radin Forcing. Using the extender sequences we combine Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing.  ...  Our work also builds on the idea of Gitik and Magidor. However, we implement the idea of adding many sequences to Radin forcing.  ... 
arXiv:math/0001121v1 fatcat:4epjmfpnffhhfj5s6numhtdlbe

Sets in Prikry and Magidor Generic Extensions [article]

Tom Benhamou, Moti Gitik
2020 arXiv   pre-print
We continue Gitik, Kanovei and Koepke's work and study sets in generic extensions by the Magidor forcing and by the Prikry forcing with non-normal ultrafilters.  ...  One of possible further directions is to extend our results from the Magidor forcing to the Radin forcing.  ...  The forcings {M I [ U ] | I ∈ P (ω o U (κ) ), I is closed} is the family of Magidor-type forcings with the coherent sequence U .In practice, Magidor-type forcings are just Magidor forcing with a subsequence  ... 
arXiv:2009.12774v2 fatcat:qsqebuumirffnjmwnxan6ugo2e

The tree property at double successors of singular cardinals of uncountable cofinality [article]

Mohammad Golshani, Rahman Mohammadpour
2017 arXiv   pre-print
Assuming the existence of a strong cardinal κ and a measurable cardinal above it, we force a generic extension in which κ is a singular strong limit cardinal of any prescribed cofinality, and such that  ...  Subsequentlly, Mitchell [11] , defined Radin forcing (of which Magidor forcing is a special case) using coherent sequences of measures. The interested reader could consult [7] for more details.  ...  Coherent Sequences and Magidor Forcing Magidor forcing for changing cofinality of a large cardinal κ to some regular δ < κ was originally defined by Magidor in [10] using a Mitchell-increasing sequence  ... 
arXiv:1612.08358v2 fatcat:gbaofrtkhvegradqyiiotygvga

Extender-based Radin forcing

Carmi Merimovich
2003 Transactions of the American Mathematical Society  
Using the extender sequences, we show how to combine the Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing.  ...  We show that this forcing satisfies a Prikry-like condition, destroys no cardinals, and has a kind of properness.  ...  Our work also builds on the idea of Gitik and Magidor. However, we implement the idea of adding many sequences to Radin forcing.  ... 
doi:10.1090/s0002-9947-03-03202-1 fatcat:zf63iguxxnfudn364yviqo4uvy

Page 1796 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
M. (1-SMTH) Magidor-like and Radin-like forcing. Ann. Pure Appl. Logic 25 (1983), no. 1, 59-72. As the author notes in his introduction, K. Prikry [Dissertationes Math.  ...  by forcing.  ... 

Diamonds, Compactness, and Measure Sequences [article]

Omer Ben-Neria
2017 arXiv   pre-print
The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of κ in a Radin generic extension.  ...  Acknowledgments: The author would like to thank Thomas Gilton and Mohammad Golshani for many valuable comments and suggestions which greatly improved the manuscript.  ...  The following result is originally due to Cummings and Woodin ( [3] ). Proposition 13. Let R( U ) be a Radin or a Magidor forcing on a cardinal κ.  ... 
arXiv:1705.01611v2 fatcat:xfzy3rmlabb6lmm7ro3u4vlxse
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