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63 件中 1 - 10 件目

年度 Year	論文題目名 Title of the articles	共著区分 Collaboration Classification
年度 Year	掲載誌名 Journal name，出版機関名 Publishing organization，巻／号 Vol./no.，頁数 Page nos.，発行年月（日） Date
2024	A Simplified Morass using Partially Frozen Finite Conditions	単著
	アカデミア　人文・自然科学編　，南山大学， 27 ， pp. 265-271 ， 2024/01
	概要（Abstract） Presented is a poset to force a simplified morass. The poset consists of finite symmetric systems. No fast functions are involved.
	備考（Remarks）
2023	Negating a partition relation by a family of simplified morasses	単著
	数理解析研究所講究録，京都大学数理解析研究所， 2261 ， pp. 78-87 ， 2023/07
	概要（Abstract） Assuming three types of morasses, a map from the edges of the third uncountable cardinal into the set of all natural numbers is constructed. The map has no large homogeneous set.
	備考（Remarks）
2022	A Fast Function at the Second Uncountable Cardinal	単著
	アカデミア　人文・自然科学編　，南山大学， 25 ， 297-306 ， 2023/01
	概要（Abstract） We consider a poset to force a club subset of the second least uncountable cardinal. Two types of non-transitive elementry substructures of a transitive set model of set theory are used. One of them is of the size the least uncountable cardinal and the other is countable.
	備考（Remarks）
2022	Forcing a Club by a Generalized Fast Function	単著
	アカデミア　人文・自然科学編　，南山大学， 23 ， 183-191 ， 2022/01
	概要（Abstract）
	備考（Remarks） We present a new proper poset that forces what we called a generalized fast function. The domain of the function results in a club subset of the least uncountable cardinal. The union of the accumulation points of the club and the singleton set of the least element of the club forms the domain of the function. The poset consists of finite conditions. As an application, we present a proper poset that forces a gap one morass of Velleman. It is still open how we approach gap two morasses of Velleman along this line of construction.
2021	Forcing the Mapping Reflection Principle by finite approximations	共著
	Arch. Math. Logic ， Springer ， Vol. 60 / no. 6 ， 737–748 ， 2021/01
	概要（Abstract） We present a new proper poset that forces the Mapping Reflection Principle of Moore. The poset consists of finite conditions and enjoys amalgamations of several conditions at a time.
	備考（Remarks）
2020	Lifting Isomorphisms in Iterated Generic Extensions	単著
	アカデミア　人文・自然科学編　，南山大学， 21 ， 307-314 ， 2021/01
	概要（Abstract） This paper deals with a simple example of Aspero-Mota type iterated forcing of the length of the second uncountable cardinal. The isomorphisms between models in the conditions are naturally lifted in the generic extensions. As a result, the Continuum Hypothesis (CH) is preserved by every proper intermediate stage of the iteration. This generalizes a result of Aspero on CH and to be compared with that of Shelah.
	備考（Remarks）
2020	Forcing continuous epsilon-chains with finite side conditions	単著
	京都大学数理解析研究所講究録，京都大学数理解析研究所， 2164 ， 142-146 ， 2020/07
	概要（Abstract） We present a poset that is of finite in nature and yet adds a continous epsilon-chain of countable models of set theory. The length of the sequence is the least uncountable cardinal. As an application, we consider the Strong Reflection Principle of Todorcevic.
	備考（Remarks）
2020	A fragment of Aspero-Mota's finitely proper forcing axiom and entangled sets of reals	共著
	Fund. Math. ， Polish Academy of Sciences ， 251, no. 1 ， 35-68. ， 2020/03
	概要（Abstract） This paper deals with a forcing axiom that is compatible with an entangled set. It turns out that the seemingly stronger notion of the entangledness here is actually equivalent to the one found in the literatures. This is due to the referee. The construction is done by an Aspero-Mota type iterated forcing and it tends to be technical.
	備考（Remarks）
2019	Partitioning the Triples of Countable Ordinals and Morasses	単著
	アカデミア　人文・自然科学編　，南山大学， 19 ， pp.165-170 ， 2020/01/31
	概要（Abstract） We deal with the negative Ramsey-type partition relation. We present a new proof of a result established by P. Erdos and R. Rado in 1956. We use a simplified morass formulated by D. Velleman in the 1980s.
	備考（Remarks）
2019	Iteratively Forcing Fast Functions	単著
	『アカデミア』人文・自然科学編，南山大学，第17号， 163-171 ， 2019/01
	概要（Abstract） This paper presents a simple example of iterated forcing that utilizes the newly developed Aspero-Mota method. Here we use only one transitive set universe and its countable elementary substructures. For any elementary substructure with a finite set of markers, we interpret it as a substructure with a specified single initial segment of the sets of ordinals of the substructure.
	備考（Remarks）

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