Let κ B be the least cardinal for which the Baire category theorem fails for the real line R. Thus κ B is the least κ such that the real line can be covered by κ many nowhere dense sets. It is shown that κ B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2 ω 1 be ℵ ω . Similar questions are considered for the ideal of measure zero sets, other (...) ω 1 saturated ideals, and the ideal of zero-dimensional subsets of R ω 1. (shrink)

Reform of the federal income tax system has become a perennial item on the domestic policy agenda of the United States, although there is considerable uncertainty over specifics. Indeed the recent report of the President's Advisory Panel on Federal Tax Reform recommended not one but two divergent policy directions. In Fundamental Tax Reform, top experts in tax policy discuss a wide range of issues raised by the prospect of significant tax reform, identifying the most critical questions and considering whether the (...) answers are known, unknown--or unknowable. The debates over tax reform usually concern the advantages and disadvantages of income-based taxation as opposed to any of the several alternative forms of consumption-based taxation. The book opens with chapters that discuss the strengths, weaknesses, and political feasibility of these options. Other chapters consider the effect of tax reform on businesses, especially their investment behavior, and include a discussion of possible problems in any transition to a consumption-based tax; international taxation issues arising in an era of globalization; and individual behavioral response to tax reform, including a view of the topic from the perspective of the relatively new field of behavioral economics. ContributorsRosanne Altshuler, Alan J. Auerbach, John W. Diamond, Harry Grubert, Arnold C. Harberger, Kevin A. Hassett, Thomas J. Kniesner, Laurence J. Kotlikoff, Edward J. McCaffery, Kathryn Newmark, David Rapson, Daniel Shaviro, Joel Slemrod, James P. Ziliak, George R. ZodrowDiscussants James Alm, Henry J. Aaron, Charles L. Ballard, Leonard E. Burman, Robert S. Chirinko, Robert D. Dietz, Malcolm Gillis, Roger H. Gordon, Jane G. Gravelle, Timothy S. Gunning, James M. Poterba, Thomas S. Neubig, Alan Viard, George Yin John W. Diamond is Edward and Hermena Kelly Fellow in Tax Policy and Adjunct Professor of Economics at the Baker Institute for Public Policy, Rice University. George R. Zodrow is Professor of Economics and Rice Scholar at the Baker Institute and International Research Fellow at the Centre for Business Taxation, Oxford University. (shrink)

Review of R. Goldwater and M. Treves, eds. Artists on Art, in Leonardo, l0 (l977), 78. Review of George Linden, Reflections on the Screen, and Paul Weiss, Cinematics, in Philosophy and Phenomenological Research, XXXVIII, 2 (December l977), 266 8.

I present a formally explicit statement of Church's celebrated argument against Carnap's analysis of belief and defend it against well-known objections by W.V.O. Quine, R.M. Martin, and Michael Dummett.

The theories Si1 and Ti1 are the analogues of Buss' relativized bounded arithmetic theories in the language where every term is bounded by a polynomial, and thus all definable functions grow linearly in length. For every i, a Σbi+1-formula TOPi, which expresses a form of the total ordering principle, is exhibited that is provable in Si+11 , but unprovable in Ti1. This is in contrast with the classical situation, where Si+12 is conservative over Ti2 w. r. t. Σbi+1-sentences. The independence (...) results are proved by translations into propositional logic, and using lower bounds for corresponding propositional proof systems. (shrink)

We define and study a new restricted consistency notion RCon ∗ for bounded arithmetic theories T 2 j . It is the strongest ∀ Π 1 b -statement over S 2 1 provable in T 2 j , similar to Con in Krajíček and Pudlák, 29) or RCon in Krajı́ček and Takeuti 107). The advantage of our notion over the others is that RCon ∗ can directly be used to construct models of T 2 j . We apply this by (...) proving preservation theorems for theories of bounded arithmetic of the following well-known kind: The ∀ Π 1 b -separation of bounded arithmetic theories S 2 i from T 2 j is equivalent to the existence of a model of S 2 i which does not have a Δ 0 b -elementary extension to a model of T 2 j . More specific, let M ⊨ Ω 1 nst denote that there is a nonstandard element c in M such that the function n ↦ 2 log c is total in M . Let BLΣ 1 b be the bounded collection schema for Σ 1 b -formulas. We obtain the following preservation results: the ∀ Π 1 b -separation of S 2 i from T 2 j is equivalent to the existence of 1. a model of S 2 i +Ω 1 nst which is 1 b -closed w.r.t. T 2 j , 2. a countable model of S 2 i + BLΣ 1 b without weak end extensions to models of T 2 j. (shrink)

Biologists, historians, lawyers, art historians, and literary critics all voice arguments in the critical dialogue about what constitutes evidence in research and scholarship. They examine not only the constitution and "blurring" of disciplinary boundaries, but also the configuration of the fact-evidence distinctions made in different disciplines and historical moments the relative function of such concepts as "self-evidence," "experience," "test," "testimony," and "textuality" in varied academic discourses and the way "rules of evidence" are themselves products of historical developments. The essays and (...) rejoinders are by Terry Castle, Lorraine Daston, Carlo Ginzburg, Ian Hacking, Mark Kelman, R. C. Lewontin, Pierre Vidal-Naquet, Mary Poovey, Donald Preziosi, Simon Schaffer, Joan W. Scott, Eve Kosofsky Sedgwick, and Barbara Herrnstein Smith. The critical responses are by Lauren Berlant, James Chandler, Jean Comaroff, Arnold I. Davidson, Harry D. harootunian, Elizabeth Helsinger, Thomas C. Holt, Francoise Meltzer, Robert J. Richards, Lawrence Rothfield, Joel Snyder, Cass R. Sunstein, and William Wimsatt. (shrink)