Itay Neeman

DKAL: Distributed-Knowledge Authorization Language

DKAL is a new declarative authorization language for distributed systems. It is based on existential fixed-point logic and is considerably more expressive than existing authorization languages in the literature. Yet its query algorithm is within the same bounds of computational complexity as e.g. that of SecPAL. DKALs communication is targeted which is beneficial for security and for liability protection. DKAL enables flexible use of functions; in particular principals can quote (to other principals) whatever has been said to them. DKAL strengthens the trust delegation mechanism of SecPAL. A novel information order contributes to succinctness. DKAL introduces a semantic safety condition that guarantees the termination of the query algorithm.

Inner models in the region of a Woodin limit of Woodin cardinals

Abstract We extend the construction of Mitchell and Steel (Fine Structure and Iteration Trees, Lecture Notes in Logic, vol. 3, Springer, Berlin, 1994) to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more. The precise level reached is that of a cardinal which is both a Woodin cardinal and a limit of cardinals strong past it.

Forcing with Sequences of Models of Two Types

We present an approach to forcing with finite sequences of models that uses models of two types. This approach builds on earlier work of Friedman and Mitchell on forcing to add clubs in cardinals larger than א1, with finite conditions. We use the two-type approach to give a new proof of the consistency of the proper forcing axiom. The new proof uses a finite support forcing, as opposed to the countable support iteration in the standard proof. The distinction is important since a proof using finite supports is more amenable to generalizations to cardinals greater than א1. MSC-2010: 03E35.

Logic of infons: The propositional case

Infons are statements viewed as containers of information (rather then representations of truth values). The logic of infons turns out to be a conservative extension of logic known as constructive or intuitionistic. Distributed Knowledge Authorization Language uses additional unary connectives “p said” and “p implied” where p ranges over principals. Here we investigate infon logic and a narrow but useful primal fragment of it. In both cases, we develop model theory and analyze the derivability problem: Does the given query follow from the given hypotheses? Our more involved technical results are on primal infon logic. We construct an algorithm for the multiple derivability problem: Which of the given queries follow from the given hypotheses? Given a bound on the quotation depth of the hypotheses, the algorithm runs in linear time. We quickly discuss the significance of this result for access control.

ARONSZAJN TREES AND FAILURE OF THE SINGULAR CARDINAL HYPOTHESIS

The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. We prove from large cardinals that the tree property at κ+ is consistent with failure of the singular cardinal hypothesis at κ.

A weak Dodd-Jensen lemma

We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice. ?

THE DOMESTIC LEVELS OF K c ARE ITERABLE

We show that the models produced by theKc construction before (if ever) it reaches a non-domestic premouse are all iterable. As a corollary we get thatPFA plus the existence of a measurable cardinal implies the existence of a non-domestic premouse.

OPTIMAL PROOFS OF DETERMINACY II

We present a general lemma which allows proving determinacy from Woodin cardinals. The lemma can be used in many different settings. As a particular application we prove the determinacy of sets in , n ≥ 1. The assumption we use to prove determinacy is optimal in the base theory of determinacy.

THE TREE PROPERTY UP TO א ω +1

Assuming ω supercompact cardinals we force to obtain a model where the tree property holds both at אω+1, and at אn for all 2 ≤ n < ω. A model with the former was obtained by Magidor–Shelah from a huge cardinal and ω supercompact cardinals above it, and recently by Sinapova from ω supercompact cardinals. A model with the latter was obtained by Cummings–Foreman from ω supercompact cardinals. Our model, where the two hold simultaneously, is another step toward the goal of obtaining the tree property on increasingly large intervals of successor cardinals. MSC-2010: 03E35, 03E05, 03E55.

Determinacy in L(ℝ)

A two-player game is said to be determined if one of the two players has a winning strategy. Determinacy for a pointclass Γ is the assertion that all perfect information two-player games of length ω on natural numbers, with payoff in Γ, are determined. Determinacy may fail for games with payoff sets constructed using the axiom of choice, but turns out in contrast to be a key property of definable sets, from which many other properties and a rich structure theory can be derived. This paper presents proofs of determinacy for definable sets, starting with determinacy for the pointclass of analytic sets, continuing through projective sets, and ending with all sets in L(ℝ). Proofs of determinacy for these pointclasses involve large cardinal axioms at the level of measurable cardinals and Woodin cardinals. The paper presents some of the theory of these large cardinals, including the relevant definitions and all results that are needed for the determinacy proofs.