Inner Models and Large Cardinals by Martin Zeman

By Martin Zeman

This quantity is an creation to internal version conception, a space of set idea that is keen on positive structural internal types reflecting huge cardinal houses of the set theoretic universe. The monograph includes a precise presentation of basic high quality constitution idea in addition to a latest method of the development of small center types, particularly these types containing at such a lot one robust cardinal, including a few of their purposes. the ultimate a part of the e-book is dedicated to a brand new procedure encompassing huge internal versions which admit many Woodin cardinals. The exposition is self-contained and doesn't imagine any targeted prerequisities, which may still make the textual content understandable not just to experts but additionally to complicated scholars in Mathematical good judgment and Set thought.

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Neatly define static phenomenology in contrast: “Static phenomenology begins from species of stable objects, both real objects (for example, natural things) and ideal objects (for example, mathematical propositions), and proceeds both noetically and noematically to investigate the complexes of immanent experiences in which these species of objects attain teleologically to givenness. In the course of such an investigation, and within the ‘phenomenological reduction,’ these objects are regarded purely as the objective correlates of modes of consciousness.

10 In Cartesian terms, I am related to the world as cogito to cogitationes: Anything belonging to the world, any spatio-temporal being, exists for me … in that I experience it, perceive it, remember it, think of it somehow, judge about it, value it, desire it, or the like … The world is for me absolutely nothing else but the world existing for and accepted by me in such a conscious cogito. It gets its whole sense, universal and specific, and its acceptance as existing, exclusively from such cogitationes.

Metaphysics fails because the framework for ultimate reality that it provides can be shown to be nothing more than a construction, a construction in which we have heavily invested. For Nietzsche there is no certainty other than the certainty of one’s own will to decide. The attempts of philosophy or religion to give meaning to life are, for Nietzsche, entirely empty, futile expressions emerging from fear in the face of an indifferent universe. ” 1 See Chapter 11 of Friedrich Nietzsche, The Anti-Christ, trans.

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