Title
Symmetric Models, Singular Cardinal Patterns, and Indiscernibles: Infinitary combinatorics without the axiom of choice,Used
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This thesis is on the topic of set theory and in particular large cardinal axioms, singular cardinal patterns, and model theoretic principles in models of set theory without the axiom of choice (ZF). A standardised setup for the technique of our main tool, symmetric forcing, is established, in order to describe models that satisfy the approximation lemma. Sets of ordinals in such models are included in some model of set theory with the axiom of choice (ZFC). This enables the partial usage of previous knowledge about models of ZFC in the proofs. Most of the models are constructed using large cardinal strength and have cardinals with large cardinal properties. With the construction of such models it is shown that if we drop the axiom of choice from our requirements and assume a certain amount of large cardinal strength, several patterns of singular cardinals are possible and model theoretic properties such as higher Chang conjectures become much weaker in consistency strength. This thesis is written in a didactic style, in the hope that it will be useful for other researchers who want to use symmetric forcing with large cardinals for consistency strength studies.
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Shipping & Returns
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We ship your order within 2–3 business days for USA deliveries and 5–8 business days for international shipments. Once your package has been dispatched from our warehouse, you'll receive an email confirmation with a tracking number, allowing you to track the status of your delivery.
Returns
To facilitate a smooth return process, a Return Authorization (RA) Number is required for all returns. Returns without a valid RA number will be declined and may incur additional fees. You can request an RA number within 15 days of the original delivery date. For more details, please refer to our Return & Refund Policy page.
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Warranty
We provide a 2-year limited warranty, from the date of purchase for all our products.
If you believe you have received a defective product, or are experiencing any problems with your product, please contact us.
This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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We accept payments with :
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