Ayant vecu en Espagne chretienne et en Espagne musulmane, en butte aux humiliations de la Croix et du Croissant, temoin de la diffusion parmi les Juifs de la philosophie greco-arabe dont il reconnait et deplore le pouvoir de seduction et les ravages qu'elle provoque, Juda Hallevi, l'un des plus grands poetes de l'Age d'or, achevera vers la fin de sa vie un ouvrage et accomplira une action d'eclat qui lui assureront une place de premier plan dans le judaisme. Defendant (...) dans un livre, devenu classique, sa foi contre la philosophie, le christianisme et l'Islam, il tentera, contrairement a la plupart des penseurs juifs du Moyen Age, de mettre en lumiere la specificite de la religion, qui cesse d'etre pour lui la version populaire allegorisee du systeme de Platon ou d'Aristote, et de fournir une interpretation de l'existence juive sur sa terre ancestrale et dans l'Exil. Ayant egalement compris que ni en Orient ni en Occident il n'existe un lieu d'espoir en qui puisse se fier, il s'arrach, non sans dechirement, a l'Espagne, sa terre natale, et bravant tous les dangers, il part pour Sion, qu'il a chantee en des vers emouvant. Mais sa mort en Egypte fait eclore la legende. (shrink)

In this work we give a complete answer as to the possible implications between some natural properties of Lebesgue measure and the Baire property. For this we prove general preservation theorems for forcing notions. Thus we answer a decade-old problem of J. Baumgartner and answer the last three open questions of the Kunen-Miller chart about measure and category. Explicitly, in \S1: (i) We prove that if we add a Laver real, then the old reals have outer measure one. (ii) We (...) prove a preservation theorem for countable-support forcing notions, and using this theorem we prove (iii) If we add ω 2 Laver reals, then the old reals have outer measure one. From this we obtain (iv) $\operatorname{Cons}(\mathrm{ZF}) \Rightarrow \operatorname{Cons}(\mathrm{ZFC} + \neg B(m) + \neg U(m) + U(c))$ . In \S2: (i) We prove a preservation theorem, for the finite support forcing notion, of the property " $F \subseteq ^\omega\omega$ is an unbounded family." (ii) We introduce a new forcing notion making the old reals a meager set but the old members of ω ω remain an unbounded family. Using this we prove (iii) $\operatorname{Cons}(\mathrm{ZF}) \Rightarrow \operatorname{Cons}(\mathrm{ZFC} + U(m) + \neg B(c) + \neg U(c) + C(c))$ . In \S3: (i) We prove a preservation theorem, for the finite support forcing notion, of a property which implies "the union of the old measure zero sets is not a measure zero set," and using this theorem we prove (ii) $\operatorname{Cons}(\mathrm{ZF}) \Rightarrow \operatorname{Cons}(\mathrm{ZFC} + \neg U(m) + C(m) + \neg C(c))$. (shrink)

The original work has been a favorite of both scholars and laypeople for its straightforward style, in contrast to other medieval writings on ethics that are largely theoretical and reflective.

The Kuzari by Judah HaLevi, the Sephardic philosopher and poet, is one of the most important statements of Jewish thought from the last thousand years. It was written as an introduction to Judaism in the form of a dialogue, primarily between the king of the Khazars and the rabbi who explains Judaism to him. The King was exploring the possibility of converting to a monotheistic religion, and the question was whether Judaism, Christianity or Islam would be his choice. The (...) King called representatives of each of the three religious traditions to explain their central beliefs and practices. (shrink)

Thank you very much, Ladies and Gentleman. I am very honored by the invitation to give a keynote address at this very informative, national meeting, before such a distinguished audience.If you made a list of the hundreds of different activities that go on during the day in a major medical center and tried to rank order them in terms of degree of difficulty, or judgment required, or risk of error, or damage that can result from an error of omission or (...) an error of commission, at the top of the list one might consider the teaching of a surgical resident at the operating table by a senior experienced surgeon, hours on end, often emotionally draining. (shrink)

It is shown that there is a subalgebra of the measure algebra forcing dominating reals. Also results are given about iterated forcing connected with random reals.

ḥeleḳ 1. Maʼamar rishon -- ḥeleḳ 2. Maʼamar sheni -- ḥeleḳ 3. Maʼamar shelishi -- ḥeleḳ 4. Maʼamar reviʻi-ḥamishi.

We show the Borel Conjecture is consistent with the continuum large.

kerekh 1-2. Maʼamarim rishon ṿe-sheni -- kerekh 3-4. Maʼamarim shelishi u-reviʻi -- kerekh 5. Maʼamar ḥamishi u-firḳe mavo.

We define the ideal with the property that a real omits all Borel sets in the ideal which are coded in a transitive model if and only if it is an amoeba real over this model. We investigate some other properties of this ideal. Strolling through the "amoeba forest" we gain as an application a modification of the proof of the inequality between the additivities of Lebesgue measure and Baire category.

In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.

If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.

In this paper we will study four forcing notions, two of them giving a minimal degree of constructibility. These constructions give answers to questions in [Ih].