We analyze the modified extender based forcing from Assaf Sharon’s PhD thesis. We show there is a bad scale in the extension and therefore weak square fails. We also present two metatheorems which give a rough characterization of when a diagonal Prikry-type forcing forces the failure of weak square.

The ability to extend a language with new syntactic forms is a powerful tool. A sufficiently flexible macro system allows programmers to build from a common base towards a language designed specifically for their problem domain. However, macro facilities that are integrated, capable, and at the same time simple enough to be widely used have been limited to the Lisp family of languages to date. ...

The extender based Prikry forcing notion is being generalized to supercompact extenders.

We show that Gitik’s short extender gap-2 forcing is of Prikry

Four premises for sperm preservation were previously outlined. The present work tested 2 of these. The first premise was that sperm mobility phenotype affects procedural efficacy. Random bred roosters were phenotyped with the sperm mobility assay. A normal frequency distribution was observed with 35% (SD = 16.4) mobile sperm. Test subjects had values >51% (high) or between 19 and 35% (below ave...

We define extender sequences, generalizing measure sequences of Radin forcing. Using the extender sequences, we show how to combine the Gitik-Magidor forcing for adding many Prikry sequenes with Radin forcing. We show that this forcing satisfies a Prikry like condition destroys no cardinals, and has a kind of properness. Depending on the large cardinals we start with this forcing can blow the p...

Our main results are: 1) every countably certified extender that coheres with the core model K is on the extender sequence of K, 2) K computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of K, 4) (joint with W. J. Mitchell) K‖κ is universal for mice of height ≤ κ whenever κ ≥ א2, 5) if there is a κ such that κ is either a si...

The objective of this study was to evaluate quality of frozen-thawed bull semen processed with extenders containing vitamin C and E as antioxidants. Pooled semen's were collected from 5 bulls and diluted to a concentration of 30 × 106 sperm/mL with citrate –egg yolk (CEY) or Tris – egg yolk (TEY) extenders. The diluted semen was divided to 5 aliquots including control and 4 experimental groups....