Inner models with large cardinal features usually obtained by forcing

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal \kappa for which 2^\kappa=\kappa^+, another for which 2^\kappa=\kappa^++ and another in which the least strongly compact cardinal is supercompact. If there is a strongly compact cardinal, then there is an inner model with a strongly compact cardinal, for which the measurable cardinals are bounded below it and another inner model W with a strongly compact cardinal \kappa, such that H_{\kappa^+}^V\subseteq HOD^W. Similar facts hold for supercompact, measurable and strongly Ramsey cardinals. If a cardinal is supercompact up to a weakly iterable cardinal, then there is an inner model of the Proper Forcing Axiom and another inner model with a supercompact cardinal in which GCH+V=HOD holds. Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between strong compactness and supercompactness. If a cardinal is strongly compact up to a weakly iterable cardinal, then there is an inner model in which the least measurable cardinal is strongly compact. If there is a weakly iterable limit \delta of <\delta-supercompact cardinals, then there is an inner model with a proper class of Laver-indestructible supercompact cardinals. We describe three general proof methods, which can be used to prove many similar results

A Note on Indestructibility and Strong Compactness

If κ &lt; λ are such that κ is both supercompact and indestructible under κ-directed closed forcing which is also (κ+,∞)-distributive and λ is 2λ supercompact, then by [3, Theorem 5], {δ &lt; κ | δ is δ+ strongly compact yet δ isn’t δ+ supercompact} must be unbounded in κ. We show that the large cardinal hypothesis on λ is necessary by constructing a model containing a supercompact cardinal κ in which no cardinal δ&gt; κ is 2δ = δ+ supercompact, κ’s supercom-pactness is indestructible under κ-directed closed forcing which is also (κ+,∞)-distributive, and for every measurable cardinal δ, δ is δ+ strongly compact iff δ is δ+ supercompact.

Formulation and Evaluation of Delayed Release Pantoprazole Sodium Enteric Coated Tablets.

The treatment of acute diseases or a chronic illness has been mostly accomplished by delivery of drugs to patients using various pharmaceutical dosage forms including tablets, capsules, pills, suppositories, creams, ointments, liquids, aerosols, and injectables as drug carriers. Drugs may be administered by variety of routes but oral administration is adopted wherever possible. There are many applications and large markets for non-oral products and the technologies that deliver them. However, if it is an applicable option, oral drug delivery will be selected in all but the most exceptional circumstances. It is safest, easiest, and most economical route of drug administration. Amongst drugs that are administered orally solid oral dosage forms i.e. tablets and capsules, represent the preferred class of products. Out of the two oral solid dosage forms, the tablets have number of advantages like tamper proof, low cost and speed of manufacturing (direct compression), ease of administration, patient compliance and flexibility in formulation etc. The present work may explore the following aspects in the future which may become a valuable assets in the field of pharmaceutical science. Manufacture Acid labile drug into formulations as cost effective & stable pharmaceutical compositon. The invitro studies can be extended to invivo studies by leading to a final conclusion of a sucessful formulation which can be marketed there after