Results for 'Sakae Yaegasi'

19 found
Order:
  1.  8
    Tennenbaum's Theorem and Unary Functions.Sakae Yaegasi - 2008 - Notre Dame Journal of Formal Logic 49 (2):177-183.
    It is well known that in any nonstandard model of $\mathsf{PA}$ (Peano arithmetic) neither addition nor multiplication is recursive. In this paper we focus on the recursiveness of unary functions and find several pairs of unary functions which cannot be both recursive in the same nonstandard model of $\mathsf{PA}$ (e.g., $\{2x,2x+1\}$, $\{x^2,2x^2\}$, and $\{2^x,3^x\}$). Furthermore, we prove that for any computable injection $f(x)$, there is a nonstandard model of $\mathsf{PA}$ in which $f(x)$ is recursive.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  2. Some Remarks on Openly Generated Boolean Algebras.Sakaé Fuchino - 1994 - Journal of Symbolic Logic 59 (1):302-310.
    A Boolean algebra B is said to be openly generated if {A: A ≤rc B, |A| = ℵ0} includes a club subset of [ B]ℵ0 . We show: (V = L). For any cardinal κ there exists an L∞κ-free Boolean algebra which is not openly generated (Proposition 4.1). (MA+(σ-closed)). Every L∞ℵa -free Boolean algebra is openly generated (Theorem 4.2). The last assertion follows from a characterization of openly generated Boolean algebras under MA+(σ-closed) (Theorem 3.1). Using this characterization we also prove (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  3.  15
    Sticks and Clubs.Sakaé Fuchino, Saharon Shelah & Lajos Soukup - 1997 - Annals of Pure and Applied Logic 90 (1):57-77.
    We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  23
    On L∞Κ-Free Boolean Algebras.Sakaé Fuchino, Sabine Koppelberg & Makoto Takahashi - 1992 - Annals of Pure and Applied Logic 55 (3):265-284.
    We study L∞κ-freeness in the variety of Boolean algebras. It is shown that some of the theorems on L∞κ-free algebras which are known to hold in varieties such as groups, abelian groups etc. are also true for Boolean algebras. But we also investigate properties such as the ccc of L∞κ-free Boolean algebras which have no counterpart in the varieties above.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  5.  19
    On Potential Embedding and Versions of Martin's Axiom.Sakaé Fuchino - 1992 - Notre Dame Journal of Formal Logic 33 (4):481-492.
  6.  5
    The Set-Theoretic Multiverse as a Mathematical Plenitudinous Platonism Viewpoint.Sakaé Fuchino - 2012 - Annals of the Japan Association for Philosophy of Science 20:49-54.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  7.  33
    On the Weak Freese–Nation Property of ?(Ω).Sakaé Fuchino, Stefan Geschke & Lajos Soukupe - 2001 - Archive for Mathematical Logic 40 (6):425-435.
    Continuing [6], [8] and [16], we study the consequences of the weak Freese-Nation property of (?(ω),⊆). Under this assumption, we prove that most of the known cardinal invariants including all of those appearing in Cichoń's diagram take the same value as in the corresponding Cohen model. Using this principle we could also strengthen two results of W. Just about cardinal sequences of superatomic Boolean algebras in a Cohen model. These results show that the weak Freese-Nation property of (?(ω),⊆) captures many (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  8.  16
    Partial Orderings with the Weak Freese-Nation Property.Sakaé Fuchino, Sabine Koppelberg & Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (1):35-54.
    A partial ordering P is said to have the weak Freese-Nation property if there is a mapping tf : P → [P]0 such that, for any a, b ε P, if a b then there exists c ε tf∩tf such that a c b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g. under CH, (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  9.  11
    Models of Real-Valued Measurability.Sakae Fuchino, Noam Greenberg & Saharon Shelah - 2006 - Annals of Pure and Applied Logic 142 (1):380-397.
    Solovay’s random-real forcing [R.M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory , Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428] is the standard way of producing real-valued measurable cardinals. Following questions of Fremlin, by giving a new construction, we show that there are combinatorial, measure-theoretic properties of Solovay’s model that do not follow from the existence of real-valued measurability.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  6
    On< I> L_< Sub>∞ Κ-Free Boolean Algebras.Sakaé Fuchino, Sabine Koppelberg & Makoto Takahashi - 1992 - Annals of Pure and Applied Logic 55 (3):265-284.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  11.  17
    On the Weak Freese-Nation Property of Complete Boolean Algebras.Sakaé Fuchino, Stefan Geschke, Saharon Shelah & Lajos Soukup - 2001 - Annals of Pure and Applied Logic 110 (1-3):89-105.
    The following results are proved: In a model obtained by adding ℵ 2 Cohen reals , there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. Modulo the consistency strength of a supercompact cardinal , the existence of a c.c.c. complete Boolean algebra without the weak Freese-Nation property is consistent with GCH. If a weak form of □ μ and cof =μ + hold for each μ >cf= ω , then the weak Freese-Nation property of 〈 P (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  12.  37
    Destructibility of Stationary Subsets of Pκλ.Sakaé Fuchino & Greg Piper - 2005 - Mathematical Logic Quarterly 51 (6):560-569.
    For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that such (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  13.  31
    On the Simplicity of the Automorphism Group ofP(Ω)/Fin.Sakaé Fuchino - 1992 - Archive for Mathematical Logic 31 (5):319-330.
    We prove that the automorphism group ofP(ω)/fin remains simple if ℵ2 Cohen reals are added to a model of ZFC+CH.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  14.  4
    Mathematics and Set Theory:数学と集合論.Sakaé Fuchino - 2018 - Journal of the Japan Association for Philosophy of Science 46 (1):33-47.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  15.  7
    A Reflection Principle As a Reverse-Mathematical Fixed Point Over the Base Theory ZFC.Sakaé Fuchino - 2017 - Annals of the Japan Association for Philosophy of Science 25:67-77.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  16.  1
    [Challenged by [Challenged by [Challenged by the Incompleteness Theorems]]] - a Review of K. Godel, "Uber Fromal Unentscheidbare Satze der Principia Mathematica Und Verwandter Systeme I", Translated and Commented by Susumu Hayashi and Mariko Yasugi , / Kazuyuki Tanaka, "Challenged by Godel".Sakaé Fuchino - 2013 - Journal of the Japan Association for Philosophy of Science 41 (1):63-80.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  17.  8
    Production et circulation dans un domaine monastique à l'époque carolingienne : l'exemple de l'abbaye de Saint-Denis.Sakae Tange - 1997 - Revue Belge de Philologie Et D’Histoire 75 (4):943-955.
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  18.  4
    À Propos des « Chartes D’Affectation de Biens » Pendant le Règne de Charles le Chauve.Sakae Tange - 2011 - Revue Belge de Philologie Et D’Histoire 89 (2):769-777.
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  19. Independent and Autonomous Peasantry Beside the Great Carolingian Domain.Sakae Tange - 2012 - Revue Belge de Philologie Et D’Histoire 90 (2).
    No categories
     
    Export citation  
     
    Bookmark